A fitting system of this type is disclosed in EP 0 705 727 B1 (corresponding to U.S. Pat. No. 5,820,218) comprising a first fitting, a second fitting and a transmission element which acts between the two fittings. Each fitting comprises a shaft piece, the rotation thereof unlocking the fitting. For adjusting the inclination of a backrest, the shaft piece is rotated by means of a first operating element on the second fitting, and a first lever located fixedly in terms of rotation thereon is pivoted. The first lever drives a second lever, which is connected fixedly in terms of rotation to the transmission element. The pivoting second lever rotates the transmission element, said second lever transmitting the rotational movement to the shaft piece of the first fitting. Both fittings are unlocked. For freely pivoting the backrest, a free-pivoting device is associated with the second fitting, said free-pivoting device being locked by means of a pivotable pawl. The pawl is opened by means of a second operating element, the pivoting-open pawl pivoting the second lever by means of a cable pull. The pivoting second lever rotates the transmission element, said second lever transmitting the rotational movement to the shaft piece of the first fitting. The first fitting is unlocked while the second fitting remains locked. The backrest inclination is memorized by means of the disclosed fitting system. When freely pivoting and subsequently pivoting back the backrest, the previously set backrest inclination is again adopted.